Direct topological insulator transitions in three dimensions are destabilized by nonperturbative effects of disorder

We reconsider the phase diagram of a three-dimensional Z₂ topological insulator in the presence of short-ranged potential disorder, with the insight that nonperturbative rare states destabilize the noninteracting Dirac semimetal critical point separating different topological phases. Based on our numerical data on the density of states, conductivity, and wave functions, we argue that the putative Dirac semimetal line is destabilized into a diffusive metal phase of finite extent due to nonperturbative effects of rare regions. We discuss the implications of these results for past and current experiments on doped topological insulators.